On one inverse problem

TL;DR

This paper investigates a specific inverse spectral problem involving quadratic pencils with complex eigenvalues, aiming to determine matrix coefficients under certain restrictions.

Contribution

It introduces a method to define matrix coefficients of quadratic pencils given complex eigenvalues with conjugates, under specific constraints.

Findings

Established a framework for inverse spectral problems with complex eigenvalues

Provided conditions under which matrix coefficients can be uniquely determined

Extended spectral theory to complex-valued eigenvalues with conjugates

Abstract

The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that these eigenvalues are complex valued and besides that they contain their conjugate ones. As is known, it is a problem of one company. We shall approach this problem on some restrictions.